Currently, Graphplan and Blackbox, which converts Graph-plan’s
plan graph into the satisfaction (SAT) problem, are
two of the most successful planners. Since Graphplan gains
its efficiency from the forward propagation of reachability
based mutual exclusion constraints (mutex) and their backward
use, it has been believed that SAT encoding will also
benefit from mutexes. In this paper, we will try to answer
two important questions: (1) Are mutual exclusions actually
useful for solution extraction in SAT encoding? (2) Are there
other useful constraints that can be propagated on the planning
graph which may help SAT solvers ? Our experiments
with systematic solvers Relsat and Satz shows that though
forward mutexes are useful in general, there are domains
in which mutex constraints can slow down search. Moreover,
we introduce the notion of backward mutex and their
propagation which is based on relevance analysis and implement
it in Blackbox. We find that the addition of relevance
based backward mutual exclusions helps speedup the Relsat
solver in solving the SAT encoding of many standard planning
problems.

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